The unit of specific heat is

Options

A. `"cal"^@ C`
B. `"cal/g".^@C`
C. cal/g
D. none of these

Answer

To determine the unit of specific heat, we can follow these steps:

### Step 1: Understand the Definition of Specific Heat
Specific heat (s) is defined as the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin).

### Step 2: Write the Formula for Heat Transfer
The formula for the heat transfer (Q) when a substance is heated is given by:
\[ Q = m \cdot s \cdot \Delta T \]
where:
- \( Q \) = heat added (in calories)
- \( m \) = mass of the substance (in grams)
- \( s \) = specific heat (in calories per gram per degree Celsius)
- \( \Delta T \) = change in temperature (in degrees Celsius)

### Step 3: Rearrange the Formula to Solve for Specific Heat
From the formula, we can rearrange it to find specific heat:
\[ s = \frac{Q}{m \cdot \Delta T} \]

### Step 4: Identify the Units
Now, we can identify the units involved in the formula:
- The unit of heat \( Q \) is in calories.
- The mass \( m \) is measured in grams.
- The change in temperature \( \Delta T \) is measured in degrees Celsius.

### Step 5: Combine the Units
Substituting the units into the equation for specific heat gives us:
\[ s = \frac{\text{calories}}{\text{grams} \cdot \text{degrees Celsius}} \]
Thus, the unit of specific heat is:
\[ \text{calorie per gram per degree Celsius} \]
or
\[ \text{calorie} \cdot \text{gram}^{-1} \cdot \text{degree Celsius}^{-1} \]

### Step 6: Choose the Correct Option
From the options provided:
1. Calorie into degree centigrade
2. Calorie upon gram into degree centigrade
3. Calorie upon gram
4. None of these

The correct answer is **Option 2: Calorie upon gram into degree centigrade**.

### Summary
The unit of specific heat is **calorie per gram per degree Celsius**.

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